Flashcard: Factored Form Quadratics

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you find the roots of a quadratic equation in factored form?

Back

To find the roots of a quadratic equation in factored form, set each factor equal to zero and solve for x.

Front

What does the term 'zeros' refer to in the context of quadratic functions?

Back

The term 'zeros' refers to the x-values where the graph of the quadratic function intersects the x-axis, also known as the roots.

Front

What is the relationship between the roots and the factors of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the factors of the equation.

Front

How can you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined by analyzing the discriminant (b² - 4ac) of the quadratic equation. If the discriminant is positive, there are two distinct zeros; if it is zero, there is one zero; and if it is negative, there are no real zeros.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you convert a quadratic equation from standard form to factored form?

Back

To convert from standard form (y = ax² + bx + c) to factored form, you can factor the quadratic expression, often using methods like factoring by grouping or applying the quadratic formula.

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it can be found using the formula x = -b/(2a) for the quadratic equation in standard form.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.